Question

Most mornings, Dr. Strangelove checks the Shuttle schedule before deciding whether to take the shuttle or book an Uber to reach for the classes. If the forecast is “on time,” the probability of actually having an on time shuttle is 80%. On the other hand, if the forecast is “not on time,” the probability of the shuttle actually coming on time is equal to 10%. The probability that the forecast is “on time” is 0.7. a) One day, he missed the forecast and the shuttle arrived on time. What is the probability that the forecast was “on time”? b) The probability of Dr. Strangelove missing the morning forecast is equal to 0.2 on any day in the year. If he misses the forecast, he will flip a fair coin to decide whether to take the shuttle or not. On any day he sees the forecast, if it says “on time” he will always take the shuttle, and if it says “not on time” he will not take the shuttle. Are the events “Dr. Strangelove is taking the shuttle” and “The forecast is not on time” independent?

Answer 1

P(on time) = P(forecast on time and on time) + P(forecast not on time and on time)

P(on time) = 0.7*80% + 0.3*10% = 0.56 + 0.03 = 0.59

(a) P(forecast on time | on time) = P(forecast on time and on time) / (P(on time))

= 0.56 / 0.59

P(forecast on time | on time) = 0.95

(b) the events “Dr. Strangelove is taking the shuttle” and “The forecast is not on time” are not independent

because if the forecast is not on time then he will not take the shuttle so one event is influencing the other therefore they are dependent

P.S. (please upvote if you find the answer satisfactory)